EP0552291B1 - Verfahren um eigenschaften und/oder zusammensetzungsdaten einer probe zu bestimmen - Google Patents

Verfahren um eigenschaften und/oder zusammensetzungsdaten einer probe zu bestimmen Download PDF

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EP0552291B1
EP0552291B1 EP91920018A EP91920018A EP0552291B1 EP 0552291 B1 EP0552291 B1 EP 0552291B1 EP 91920018 A EP91920018 A EP 91920018A EP 91920018 A EP91920018 A EP 91920018A EP 0552291 B1 EP0552291 B1 EP 0552291B1
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sample
spectra
calibration
spectrum
data
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EP0552291A4 (en
EP0552291A1 (de
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Jon Steven Gethner
Terry Ray Todd
James Milton Brown
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ExxonMobil Technology and Engineering Co
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Exxon Research and Engineering Co
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R35/00—Testing or calibrating of apparatus covered by the other groups of this subclass
    • G01R35/005—Calibrating; Standards or reference devices, e.g. voltage or resistance standards, "golden" references
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
    • G01N21/31—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry
    • G01N21/35—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light
    • G01N21/359—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light using near infrared light
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/16—Spectrum analysis; Fourier analysis
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
    • G01N21/31—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry
    • G01N21/35—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light
    • G01N21/3577—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light for analysing liquids, e.g. polluted water
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/22—Fuels; Explosives

Definitions

  • This invention relates to a method of estimating unknown property and/or composition data (also referred to herein as "parameters") of a sample.
  • property and composition data are chemical composition measurements (such as the concentration of individual chemical components as, for example, benzene, toluene, xylene, or the concentrations of a class of compounds as, for example, paraffins), physical property measurements (such as density, index of refraction, hardness, viscosity, flash point, pour point, vapor pressure), performance property measurement (such as octane number, cetane number, combustibility), and perception (smell/odor, color).
  • chemical composition measurements such as the concentration of individual chemical components as, for example, benzene, toluene, xylene, or the concentrations of a class of compounds as, for example, paraffins
  • physical property measurements such as density, index of refraction, hardness, viscosity, flash point, pour point, vapor pressure
  • performance property measurement such as oc
  • the infrared (12500-400 cm -1 ) spectrum of a substance contains absorption features due to the molecular vibrations of the constituent molecules.
  • the absorptions arise from both fundamentals (single quantum transitions occurring in the mid-infrared region from 4000-400 cm -1 ) and combination bands and overtones (multiple quanta transitions occurring in the mid- and the near-infrared region from 12500-4000 cm -1 ).
  • the position (frequency or wavelength) of these absorptions contain information as to the types of molecular structures that are present in the material, and the intensity of the absorptions contains information about the amounts of the molecular types that are present.
  • each constituent In complex mixtures, each constituent generally gives rise to multiple absorption features corresponding to different vibrational motions. The intensities of these absorptions will all vary together in a linear fashion as the concentration of the constituent varies. Such features are said to have intensities which are correlated in the frequency (or wavelength) domain. This correlation allows these absorptions to be mathematically distinguished from random spectral measurement noise which shows no such correlation.
  • the linear algebra computations which separate the correlated absorbance signals from the spectral noise form the basis for techniques such as Principal Components Regression (PCR) and Partial Least Squares (PLS).
  • PCA Principal Components Regression
  • PLS Partial Least Squares
  • PCR and PLS have been used to estimate elemental and chemical compositions and to a lesser extent physical or thermodynamic properties of solids and liquids based on their mid- or near-infrared spectra.
  • These methods involve: [1] the collection of mid- or near-infrared spectra of a set of representative samples; [2] mathematical treatment of the spectral data to extract the Principal Components or latent variables (e.g. the correlated absorbance signals described above); and [3] regression of these spectral variables against composition and/or property data to build a multivariate model.
  • the analysis of new samples then involves the collection of their spectra, the decomposition of the spectra in terms of the spectral variables, and the application of the regression equation to calculate the composition/properties.
  • the method of the present invention is of particular practical importance is the analysis of hydrocarbon test samples or for ascertaining the hydrocarbon content of a hydrocarbon/water mixture, whether in phase separated or emulsion form.
  • the present invention provides a method for recalibrating an analyzer, which method uses a correlation between calibration sample spectra and a property and/or composition data for estimating that property and/or composition data of a test sample, comprising
  • test sample for which the result of the check in step (c) is negative i.e. the measured spectrum is not within the range of calibration sample spectra in the model
  • the model is adapted to allow the data separately determined in this way, together with the corresponding measured spectral data, to be entered into the model database, so that the model thereby becomes updated with this additional data, so as to enlarge the predictive capability of the model.
  • the model "learns" from identification of a test sample for which it cannot perform a reliable prediction, so that next time a similar sample is tested containing chemical species of the earlier sample (and assuming any other chemical species it contains correspond to those of other calibration samples in the model), a reliable prediction of property and/or composition data for that similar sample will be made.
  • the predictive model can be based on principal components analysis or partial least squares analysis of the calibration sample spectra.
  • whether or not the measured spectrum of the test sample is within the range of the calibration sample spectra in the model can be determined in the following manner.
  • a simulated spectrum for the test sample is determined by deriving coefficients for the measured test spectrum from the dot (scalar) products of the measured test spectrum with each of the model eigenspectra and by adding together the model eigenspectra scaled by the corresponding coefficient.
  • This comparison is made by determining a residual spectrum as the difference between the simulated spectrum and the measured spectrum, by calculating the Euclidean norm by summing the squares of the magnitudes of the residual spectrum at discrete frequencies, and by evaluating the magnitude of the Euclidean norm.
  • a large value, determined with reference to a preselected threshold distance, is indicative that the required data prediction of the test sample cannot accurately be made, while a Euclidean norm lower than the threshold indicates an accurate prediction can be made.
  • rule-based check is pattern recognition techniques and/or comparison with spectra of computerized spectral libraries.
  • the calibration sample spectra may contain spectral data due to the measurement process itself e.g. due to baseline variations and/or ex-sample interferences (such as due to water vapor or carbon dioxide).
  • This measurement process spectral data can be removed from the calibration sample spectra prior to defining the predictive model by orthogonalizing the calibration sample spectra to one or more spectra modeling the measurement process data. This will be described in further detail herein below under the heading "CONSTRAINED PRINCIPAL SPECTRA ANALYSIS (CPSA)".
  • the property and/or compositions data prediction may be an extrapolation from the range of data covered by the calibration samples used for forming the predictive model. It is therefore preferred that the Mahalanobis distance is determined for the measured spectrum and the test sample "accepted" from this further test if the magnitude of the Mahalanobis distance is below an appropriate predetermined amount selected by the analyst. If the calculated Mahalanobis distance is above the appropriate predetermined amount, a similar response as described hereinabove for a negative check is initiated.
  • Another statistical check is to ascertain whether the test sample is lying in a region in which the number of calibration samples in the predictive model is sparse. This check can be made by calculating the Euclidean norm derived for each test sample/calibration sample pair and comparing the calculated Euclidean norms with a threshold value which, if exceeded, indicates that the sample has failed to pass this additional statistical check. In which case, a similar response as described hereinabove for a negative check is initiated.
  • the method disclosed herein finds particular application to on-line estimation of property and/or composition data of hydrocarbon test samples. Conveniently and suitably, all or most of the above-described steps are performed by a computer system of one or more computers with minimal or no operator interaction required.
  • CPSA Constrained Principal Spectra Analysis
  • the present invention can employ any numerical analysis technique (such as PCR, PLS or MLR) through which the predictive model can be obtained to provide an estimation of unknown property and/or composition data. It is preferred that the selected numerical analysis technique be CPSA.
  • CPSA is described in detail in the present assignees copending U.S. patent application 597,910 of James M. Brown, now US-A-5 121 337.
  • the present invention provides apparatus for estimating property and/or composition data of a hydrocarbon test sample, which includes a means for recalibration, said apparatus comprising:
  • CPSA Constrained Principal Spectra Analysis
  • the spectral data of a number ( n ) of calibration samples is corrected for the effects of data arising from the measurement process itself (rather than from the sample components).
  • the spectral data for n calibration samples is quantified at f discrete frequencies to produce a matrix X (of dimension f by n ) of calibration data.
  • the first step in the method involves producing a correction matrix U m of dimension f by m comprising m digitized correction spectra at the discrete frequencies f , the correction spectra simulating data arising from the measurement process itself.
  • the other step involves orthoganalizing X with respect to U m to produce a corrected spectra matrix X c whose spectra are orthogonal to all the spectra in U m . Due to this orthogonality, the spectra in matrix X c are statistically independent of spectra arising from the measurement process itself. If (as would normally be the case) the samples are calibration samples used to build a predictive model interrelating known property and composition data of the n samples and their measured spectra so that the model can be used to estimate unknown property and/or composition data of a sample under consideration from its measured spectrum, the estimated property and/or composition data will be unaffected by the measurement process itself.
  • spectra can be absorption spectra and the preferred embodiments described below all involve measuring absorption spectra.
  • this is to be considered as exemplary and not limiting on the scope of the invention as defined by the appended claims, since the method disclosed herein can be applied to other types of spectra such as reflection spectra and scattering spectra (such as Raman scattering).
  • NIR near-infrared
  • MIR mid-infrared
  • the data arising from the measurement process itself are due to two effects.
  • the first is due to baseline variations in the spectra.
  • the baseline variations arise from a number of causes such as light source temperature variations during the measurement, reflectance, scattering or absorbances from the cell windows, and changes in the temperature (and thus the sensitivity) of the instrument detector. These baseline variations generally exhibit spectral features which are broad (correlate over a wide frequency range).
  • the second type of measurement process signal is due to ex-sample chemical compounds present during the measurement process, which give rise to sharper line features in the spectrum.
  • this type of correction generally includes absorptions due to water vapor and/or carbon dioxide in the atmosphere in the spectrometer.
  • sample refers to that material upon which property and/or component concentration measurements are conducted for the purpose of providing data for the model development.
  • contaminant we refer to any material which is physically added to the sample after the property/component measurement but before or during the spectral measurement.
  • the present corrective method can be applied to correct only for the effect of baseline variations, in which case these variations can be modeled by a set of preferably orthogonal, frequency (or wavelength) dependent polynomials which form the matrix U m of dimension f by m where m is the order of the polynomials and the columns of U m are preferably orthogonal polynomials, such as Legendre polynomials.
  • the corrective method can be applied to correct only for the effect of ex-sample chemical compounds (e.g. due to the presence in the atmosphere of carbon dioxide and/or water vapor).
  • the spectra that form the columns of U m are preferably orthogonal vectors that are representative of the spectral interferences produced by such chemical compounds.
  • both baseline variations and ex-sample chemical compounds are modeled in the manner described to form two correction matrices U p of dimension f by p and X s , respectively. These matrices are then combined into the single matrix U m , whose columns are the columns of U p and X s arranged side-by-side.
  • the spectra or columns of U m are all mutually orthogonal.
  • the production of the matrix U m having mutually orthogonal spectra or columns can be achieved by firstly modeling the baseline variations by a set of orthogonal frequency (or wavelength) dependent polynomials which are computer generated simulations of the baseline variations and form the matrix U p , and then at least one, and usually a plurality, of spectra of ex-sample chemical compounds (e.g. carbon dioxide and water vapor) which are actual spectra collected on the instrument, are supplied to form the matrix X s .
  • ex-sample chemical compounds e.g. carbon dioxide and water vapor
  • the sample spectral data in the matrix X will include not only spectral data due to the measurement process itself but also data due to noise. Therefore, once the matrix X (dimension f by n ) has been orthogonalized with respect to the correction matrix U m (dimension f by m ), the resulting corrected spectral matrix X c will still contain noise data. This can be removed in the following way.
  • the principal components that correspond to noise in the spectral measurements in the original n samples will have singular values which are small in magnitude relative to those due to the wanted spectral data, and can therefore be distinguished from the principal components due to real sample components.
  • the next step in the method involves removing from U , ⁇ and V the k + 1 through n principal components that correspond to the noise, to form the new matrices U ', ⁇ ' and V ' of dimensions f by k, k by k and n by k , respectively.
  • the resulting matrix corresponding with the earlier corrected spectra matrix X c , is free of spectral data due to noise.
  • the spectral noise level is known from experience with the instrument. From a visual inspection of the eigenspectra (the columns of matrix U resulting from the singular value decomposition), a trained spectroscopist can generally recognize when the signal levels in the eigenspectra are comparable with the noise level. By visual inspection of the eigenspectra, an approximate number of terms, k, to retain can be selected.
  • Models can then be built with, for example, k -2, k - 1, k, k + 1, k + 2 terms in them and the standard errors and PRESS (Predictive Residual Error Sum of Squares) values are inspected. The smallest number of terms needed to obtain the desired precision in the model or the number of terms that give the minimum PRESS value is then selected. This choice is made by the spectroscopist, and is not automated.
  • a Predicted Residual Error Sum of Squares is calculated by applying a predictive model for the estimation of property and/or component values for a test set of samples which were not used in the calibration but for which the true value of the property or component concentration is known.
  • a PRESS value can be calculated using a cross validation procedure in which one or more of the calibration samples are left out of the data matrix during the calibration, and then analyzed with the resultant model, and the procedure is repeated until each sample has been left out once.
  • the polynomials that are used to model background variations are merely one type of correction spectrum.
  • the difference between the polynomials and the other "correction spectra" modeling ex-sample chemical compounds is twofold.
  • the polynomials may conveniently be computer-generated simulations of the background (although this is not essential and they could instead be simple mathematical expressions or even actual spectra of background variations) and can be generated by the computer to be orthogonal.
  • the polynomials may be Legendre polynomials which are used in the actual implementation of the correction method since they save computation time. There is a well-known recursive algorithm to generate the Legendre polynomials (see, for example, G.
  • each row of the U p matrix corresponds to a given frequency (or wavelength) in the spectrum.
  • the columns of the U p matrix will be related to this frequency.
  • the elements of the first column would be a constant
  • the elements of the second column would depend linearly on the frequency
  • the elements of the third column would depend on the square of the frequency, etc.
  • the exact relationship is somewhat more complicated than that if the columns are to be orthogonal.
  • the Legendre polynomials are generated to be orthonormal, so that it is not necessary to effect a singular value decomposition or a Gram-Schmidt orthogonalization to make them orthogonal.
  • any set of suitable polynomial terms could be used, which are then orthogonalized using singular value decomposition or a Gram-Schmidt orthogonalization.
  • actual spectra collected on the instrument to simulate background variation can be used and orthogonalized via one of these procedures.
  • the other "correction spectra" are usually actual spectra collected on the instrument to simulate interferences due to ex-sample chemical compounds, e.g. the spectrum of water vapor, the spectrum of carbon dioxide vapor, or the spectrum of the optical fiber of the instrument.
  • Computer generated spectra could be used here if the spectra of water vapor, carbon dioxide, etc. can be simulated.
  • the polynomials are generated first, the ex-sample chemical compound "correction spectra" are orthogonalized to the polynomials, and then the correction vectors are generated by performing a singular value decomposition (described below) on the orthogonalized "correction spectra".
  • a preferred way of performing the correction for measurement process spectral data is firstly to generate the orthogonal set of polynomials which model background variations, then to orthoganalize any "correction spectra" due to ex-sample chemical compounds (e.g. carbon dioxide and/or water vapor) to this set to produce a set of "correction vectors", and finally to orthogonalize the resultant "correction vectors" among themselves using singular value decomposition.
  • the final number of "correction vectors" will be less than the number of initial "correction spectra”.
  • the ones eliminated correspond with the measurement noise.
  • principal components analysis PCA is being performed on the orthogonalized "correction spectra” to separate the real measurement process data being modeled from the random measurement noise.
  • the columns of the correction matrix U m do not have to be mutually orthogonal for the correction method to work, as long as the columns of the data matrix X are orthogonalized to those of the correction matrix U m .
  • the steps for generating the U m matrix to have orthogonal columns is performed to simplify the computations required in the orthogonalization of the spectral data X of the samples relative to the correction matrix U m , and to provide a set of statistically independent correction terms that can be used to monitor the measurement process.
  • the next step is to orthogonalize X with respect to U m to produce a corrected spectra matrix X c whose spectra are each orthogonal to all the spectra in U m .
  • the method further requires that c property and/or composition data are collected for each of the n calibration samples to form a matrix Y of dimension n by c (c ⁇ 1).
  • a predictive model is determined correlating the elements of matrix Y to matrix X c . Different predictive models can be used, as will be explained below.
  • the property and/or composition estimating method further requires measuring the spectrum of the sample under consideration at the f discrete frequencies to form a matrix of dimension f by 1.
  • the unknown property and/or composition data of the samples is then estimated from its measured spectrum using the predictive model.
  • each property and/or component is treated separately for building models and produces a separate f by 1 prediction vector.
  • the prediction is just the dot product of the unknown spectrum and the prediction vector.
  • the prediction involves multiplying the spectrum matrix (a vector of dimension f can be considered as a 1 by f matrix) by the prediction matrix to produce a 1 by c vector of predictions for the c properties and components.
  • This calculation which is a constrained form of the K-matrix method, is more restricted in application, since the required inversion of Y t Y requires that Y contain concentration values for all sample components, and not contain property data.
  • correction matrix U m and in orthogonalizing the spectral data matrix X to U m are twofold: Firstly, predictive models based on the resultant corrected data matrix X c are insensitive to the effects of background variations and ex-sample chemical components modeled in U m , as explained above. Secondly, the dot (scalar) products generated between the columns of U m and those of X contain information about the magnitude of the background and ex-sample chemical component interferences that are present in the calibration spectra, and as such, provide a measure of the range of values for the magnitude of these interferences that were present during the collection of the calibration spectral data.
  • the dot products of the columns of U m with those of the spectral data matrix X contain information about the degree to which the measurement process data contribute to the individual calibration spectra. This information is generally mixed with information about the calibration sample components.
  • the dot product of a constant vector (a first order polynomial) will contain information about the total spectral integral, which is the sum of the integral of the sample absorptions, and the integral of the background.
  • the information about calibration sample components is, however, also contained in the eigenspectra produced by the singular value decomposition of X c . It is therefore possible to remove that portion of the information which is correlated to the sample components from the dot products so as to recover values that are uncorrelated to the sample components, i.e. values that represent the true magnitude of the contributions of the measurement process signals to the calibration spectra. This is accomplished by the following steps:
  • the performance of the above disclosed correction method and method of estimating the unknown property and/or composition data of the sample under consideration involves extensive mathematical computations to be performed.
  • such computations are made by computer means comprising a computer or computers, which is connected to the instrument.
  • the computer means receives the measured output spectrum of the Calibration sample, ex-sample chemical compound or test sample.
  • the computer means stores the calibration spectra to form the matrix X , calculates the correction matrix U m , and orthogonalizes X with respect to the correction matrix U m .
  • the computer means operates in a storing mode to store the c known property and/or composition data for the n calibration samples to form the matrix Y of dimension n by c ( c ⁇ 1).
  • the computer means determines, in conjunction with the operator, a predictive model correlating the elements of matrix Y to those of matrix X c .
  • the computer means is arranged to operate in a prediction mode in which it estimates the unknown property and/or compositional data of the sample under consideration from its measured spectrum using the determined predictive model correlating the elements of matrix Y to those of matrix X c .
  • the steps involved according to a preferred way of making a prediction of property and/or composition data of a sample under consideration can be set out as follows. Firstly, a selection of samples for the calibration is made by the operator or a laboratory technician. Then, in either order, the spectra and properties/composition of these samples need to be measured, collected and stored in the computer means by the operator and/or laboratory technician, together with spectra of ex-sample chemical compounds to be used as corrections. In addition, the operator selects the computer-generated polynomial corrections used to model baseline variations.
  • the computer means generates the correction matrix U m and then orthogonalizes the calibration sample spectra (matrix X ) to produce the corrected spectral matrix X c and, if PCR is used, performs the singular value decomposition on matrix X c .
  • the operator has to select (in PCR) how many of the principal components to retain as correlated data and how many to discard as representative of (uncorrelated) noise. Alternatively, if the PLS technique is employed, the operator has to select the number of latent variables to use.
  • MLR is used to determine the correlation between the corrected spectral matrix X c and the measured property and/or composition data Y . If MLR is used to determine the correlation between the corrected spectral matrix X c and the measured property and/or composition data Y , then a selection of frequencies needs to be made such that the number of frequencies at which the measured spectra are quantized is less than the number of calibration samples. Whichever technique is used to determine the correlation (i.e. the predictive model) interrelating X c and Y , having completed the calibration, the laboratory technician measures the spectrum of the sample under consideration which is used by the computer means to compute predicted property and/or composition data based on the predictive model.
  • the object of Principal Components Analysis is to isolate the true number of independent variables in the spectral data so as to allow for a regression of these variables against the dependent property/composition variables.
  • the spectral data matrix, X contains the spectra of the n samples to be used in the calibration as columns of length f, where f is the number of data points (frequencies or wavelengths) per spectrum.
  • the object of PCA is to decompose the f by n X matrix into the product of several matrices.
  • U will be referred to as the eigenspectrum matrix since the individual column-vectors of U (the eigenspectra ) are of the same length, f, as the original calibration spectra.
  • the term eigenvectors will only be used to refer to the V matrix.
  • Equations 2 and 3 imply that both the eigenspectra and eigenvectors are orthonormal.
  • the U and ⁇ are matrices are combined into a single matrix. In this case, the eigenspectra are orthogonal but are normalized to the singular values.
  • the object of the variable reduction is to provide a set of independent variables (the Principal Components) against which the dependent variables (the properties or compositions) can be regressed.
  • the objective of the PCA is to separate systematic (frequency correlated) signal from random noise.
  • the eigenspectra corresponding to the larger singular values represent the systematic signal, while those corresponding to the smaller singular values represent the noise.
  • these noise components will be eliminated from the analysis before the prediction vectors are calculated. If the first k ⁇ n eigenspectra are retained, the matrices in equation 1 become U ' (dimension f by k ) , ⁇ ' (dimension k by k ) and V ' (dimension n by k ).
  • X U' ⁇ 'V' t + E where E is an f by n error matrix.
  • Equation 6 shows how the prediction vector, P , is used in the analysis of an unknown spectrum.
  • the unknown spectrum can be separated as the sum of two terms, the spectrum due to the components in the unknown, x c , and the measurement process related signals for which we want to develop constraints, x s .
  • the resulting prediction vector will also be orthogonal, and the prediction will be insensitive to the measurement process signal.
  • This orthogonalization procedure serves as the basis for the Constrained Principal Spectra Analysis algorithm.
  • U p is a matrix of dimension f by p where p is the maximum order (degree minus one) of the polynomials, and it contains columns which are orthonormal Legendre polynomials defined over the spectral range used in the analysis.
  • the polynomials are intended to provide constraints for spectral baseline effects.
  • the user may supply spectra representative of other measurement process signals (e.g. water vapor spectra).
  • X c U c ⁇ c V c t
  • the resulting predictive model is thus insensitive to the modeled measurement process signals.
  • results of the procedure described above are mathematically equivalent to including the polynomial and correction terms as spectra in the data matrix, and using a constrained least square regression to calculate the B matrix in equation 12.
  • the constrained least square procedure is more sensitive to the scaling of the correction spectra since they must account for sufficient variance in the data matrix to be sorted into the k eigenspectra that are retained in the regression step.
  • the Constrained Principal Spectra Analysis method allows measurement process signals which are present in the spectra of the calibration samples, or might be present in the spectra of samples which are latter analyzed, to be modeled and removed from the data (via a Gram-Schmidt orthogonalization procedure) prior to the extraction of the spectral variables which is performed via a Singular Value Decomposition (16).
  • the spectral variables thus obtained are first regressed against the pathlengths for the calibration spectra to develop a model for independent estimation of pathlength.
  • the spectral variables are rescaled to a common pathlength based on the results of the regression and then further regressed against the composition/property data to build the empirical models for the estimation of these parameters.
  • the spectra are collected and decomposed into the constrained spectral variables, the pathlength is calculated and the data is scaled to the appropriate pathlength, and then the regression models are applied to calculate the composition/property data for the new materials.
  • the orthogonalization procedure ensures that the resultant measurements are constrained so as to be insensitive (orthogonal) to the modeled measurement process signals.
  • the internal pathlength calculation and renormalization automatically corrects for pathlength or flow variations, thus minimizing errors due to data scaling.
  • the development of the empirical model consists of the following steps:
  • the single drawing is a flow chart indicating one preferred way of performing the method of this invention.
  • the steps described above allow the estimation of property and/or composition parameters by performing on-line measurements of the absorbance spectrum of a fluid or gaseous process stream.
  • Mathematical analysis provides high quality estimates of the concentration of chemical components and the concentrations of classes of chemical components. Physical and performance parameters which are directly or indirectly correlated to chemical component concentrations are estimable. Conditions for the measurement of the absorbance spectra are specified so as to provide redundant spectral information thereby allowing the computation of method diagnostic and quality assurance measures.
  • the steps comprising the methodology are performed in an integrative manner so as to provide continuous estimates for method adjustment, operations diagnosis and automated sample collection.
  • Different aspects of the methodology are set out below in numbered paragraphs (1) to (10).

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Claims (9)

  1. Verfahren zur Rekalibrierung einer Analysevorrichtung, bei dem eine Korrelation zwischen den Spektren von Kalibrierungsproben und einer Eigenschaft und/oder Zusammensetzungsdaten zur Abschätzung dieser Eigenschaft und/oder von Zusammensetzungsdaten einer Testprobe verwendet werden, wobei
    (a) eine Spektralmessung mit der Testprobe durchgeführt wird,
    (b) die Eigenschaft und/oder die Zusammensetzungsdaten der Testprobe aus ihrem gemessenen Spektrum bestimmt werden/wird, wobei die Bestimmung anhand der Korrelation der Spektren der Kalibrierungsproben zu dieser bekannten Eigenschaft und/oder diesen bekannten Zusammensetzungsdaten der Kalibrierungsproben vorgenommen wird,
    (c) die Spektren der Kalibrierungsproben dahingehend verglichen werden, ob das gemessene Spektrum im Bereich der Spektren der Kalibrierungsproben liegt oder nicht,
    (d) die Testprobe isoliert wird, wenn das gemessene Spektrum nicht innerhalb der Korrelation zwischen diesen Spektren der Kalibrierungsproben und der Eigenschaft und/oder den Zusammensetzungsdaten liegt,
    (e) diese Testprobe aus Schritt (d) durch ein separates Verfahren analysiert wird, um die Eigenschaft und/oder die Zusammensetzungsdaten zu bestätigen, und
    (f) die Analysevorrichtung mit diesen Daten und mit den Spektralmeßdaten, die durch Durchführung der Spektralmessung mit der Testprobe von Schritt (d) erhalten worden sind, rekalibriert wird.
  2. Verfahren nach Anspruch 1, bei dem die Spektralmessung der Testprobe im Infrarotbereich durchgeführt wird.
  3. Verfahren nach einem der beiden vorhergehenden Ansprüche, für das das prädikative Modell Eigenvektor-basiert ist, wobei ein simuliertes Spektrum für die Testprobe bestimmt wird, indem die Koeffizienten für das gemessene Testspektrum aus den Punktprodukten des gemessenen Testspektrums mit jedem der Modelleigenspektren abgeleitet wird und die durch die entsprechenden Koeffizienten skalierten Modelleigenspektren miteinander addiert werden, und bei dem ein Vergleich zwischen dem simulierten Spektrum und dem gemessenen Spektrum als Abschätzung vorgenommen wird, ob das gemessene Spektrum im Bereich der Spektren der Kalibrierungsproben in dem Modell ist oder nicht.
  4. Verfahren nach Anspruch 3, bei dem der Vergleich zwischen dem simulierten Spektrum und dem gemessenen Spektrum vorgenommen wird, indem ein Restspektrum als die Differenz zwischen dem simuliertren Spektrum und dem gemessenen Spektrum bestimmt wird, indem die euklidische Norm berechnet wird, wobei die Quadrate der Magnituden des Restspektrums bei diskreten Frequenzen summiert werden und indem die Magnitude der euklidischen Norm ausgewertet wird.
  5. Verfahren nach Anspruch 4, bei dem der Mahalanobis-Abstand aus dem gemessenen Spektrum bestimmt wird und die Testprobe isoliert wird, wenn die Magnitude des bestimmten Mahalano-bis-Abstandes anzeigt, daß die Abschätzung der Eigenschaft und/oder der Zusammensetzungsdaten der Testprobe eine Extrapolation aus dem Bereich von Daten ist, der durch die Kalibrierungsproben abgedeckt ist.
  6. Verfahren nach Anspruch 5, bei dem ferner die euklidische Norm berechnet wird, die sich von jedem Testprobe/Kalibrierungsprobe-Paar ableitet, und die berechneten euklidischen Normen mit einem vorbestimmten Schwellenwert verglichen werden, um so die Testprobe zu isolieren, wenn der Schwellenwert überschritten wird.
  7. Verfahren nach einem der vorhergehenden Ansprüche, bei dem Daten in den Spektren der Kalibrierungsproben aufgrund des Meßverfahrens selbst daraus entfernt werden, bevor das prädikative Modell definiert wird, indem die Spektren der Kalibrierungsproben zu einem oder mehreren Spektren orthogonalisiert werden, die die Meßverfahrensdaten modellieren.
  8. Verfahren nach einem der vorhergehenden Ansprüche, bei dem die Probe eine Kohlenwasserstoff/Wasser-Mischung ist und die Abschätzung eine Abschätzung des Kohlenwasserstoffgehaltes oder des Wassergehaltes dieser Mischung ist.
  9. Vorrichtung zur Abschätzung der Eigenschaft und/oder von Zusammensetzungsdaten einer Kohlenwasserstofftestprobe, die Mittel zur Rekalibrierung umfaßt, wobei die Vorrichtung umfaßt:
    (a) Spektrometermittel zur Durchführung einer Spektralmessung mit einer Testprobe,
    (b) Rechenmittel (i) zur Abschätzung der Eigenschaft und/oder von Zusammensetzungsdaten der Testprobe aus ihrem gemessenen Spektrum, wobei die Bestimmung aus der Korrelation von Spektren der Kalibrierungsproben zu der bekannten Eigenschaft und/oder den bekannten Zusammensetzungsdaten für diese Kalibrierungsproben vorgenommen wird, (ii) zur Bestimmung, auf Basis einer Überprüfung des gemessenen Spektrums gegen die Spektren der Kalibrierungsproben, ob das gemessene Spektrum im Bereich der Spektren der Kalibrierungsproben liegt oder nicht,
    (c) Mittel zur Erzeugung einer Reaktion auf negative Ergebnisse durch Isolierung dieser Testprobe,
    (d) Mittel zur Analysierung dieser Testprobe von Schritt (c) zur Bestätigung ihrer Eigenschaft und/oder ihrer Zusammensetzungsdaten und
    (e) Mittel zur Eingabe solcher in den Rechner eingegebenen Daten zur Speicherung darin, so daß die Analysevorrichtung dadurch entsprechend diesen Daten aktualisiert wird.
EP91920018A 1990-10-12 1991-10-09 Verfahren um eigenschaften und/oder zusammensetzungsdaten einer probe zu bestimmen Expired - Lifetime EP0552291B1 (de)

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MY107650A (en) 1996-05-30
CA2093015C (en) 1999-12-21
JPH06502247A (ja) 1994-03-10
EP0552291A4 (en) 1994-10-26
CA2093015A1 (en) 1992-04-13
DE69128357D1 (de) 1998-01-15
US5446681A (en) 1995-08-29
EP0552291A1 (de) 1993-07-28
JP3130931B2 (ja) 2001-01-31
SG45468A1 (en) 1998-01-16
DE69128357T2 (de) 1998-07-16

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